Streaming Estimation for the Spectral Density"

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Recent technological innovations have resulted in a large increase in both data generation and data collection capabilities in many application areas, especially given the many advances in real-time information capture. Classical approaches for analysis and modelling require the data to be stored and read before it can be processed. Depending on the speed at which the data is being collected, this could result in our algorithms and models requiring a prohibitive amount of memory and computational power. Furthermore, in real world applications, the data generating process has the possibility of undergoing changes as the data is being collected. This presents another shortcoming of classical algorithms. They usually have a baked-in assumption that the generating process does not change and thus are unsuited for the task once we relax this assumption.This project falls within the EPSRC research areas for Digital Signal Processing, Statistics and Applied probability. We aim to develop methodology designed to process high frequency data, while also retaining a level of adaptability that allows us to deal with changes in the underlying random process. These methods will enable the analysis of time series as they are being observed and thus give us the ability to react to changes in real time. This is particularly useful in areas such as cyber-security, where anomalous behaviour deviating from the norm needs to be detected and investigated as soon as possible. Such a problem involves having the best possible up-to-date estimate for what the norm is, while also being able to judge any given set of datapoints as anomalous.In this project, we plan to develop methodology specifically aimed at estimating the spectral density of a time series as it evolves during the data collection process. With the spectral density capturing the vast majority of the information regarding a random data generating process, these algorithms would enable us to track changes in both the long-term seasonality and the short-term trends. Areas of current focus are non-parametric change-point detection and multivariate time series analysis. The latter we plan to extend by incorporating graph prediction and network analysis. At present, seasonality has rarely been used to analyse the underlying structure of a network. In our work we look to address this shortcoming in the literature and develop new tools for network analysis. To maximise the impact of our work, we will also develop open-source software - with documentation and demonstrations - that we will share online.